Finding the general solution to a differential equation

1. Dec 8, 2009

clarineterr

1. The problem statement, all variables and given/known data
$$\frac{d^{2}y}{dt}$$ +4$$\frac{dy}{dt}$$+20y=e$$^{-2t}$$(sin4t+cos4t)

2. Relevant equations

3. The attempt at a solution

The solution to the homogeneous equation: $$\frac{d^{2}y}{dt}$$ +4$$\frac{dy}{dt}$$+20y=0 is

y= k1e$$^{-2t}$$cos4t +k2e$$^{-2t}$$sin4t

Then I guessed ae$$^{-2+4i}$$ as a possible solution and it didn't work, and that's where I'm stuck.

2. Dec 8, 2009

LCKurtz

Since the complementary solution yc= e-2t(Acos(4t) + Bsin(4t)) is repeated in the non-homogeneous term, for your particular solution try

yp = te-2t(Ccos(4t) + Dsin(4t))

3. Dec 9, 2009

clarineterr

Nope...didn't work. :(

4. Dec 9, 2009

LCKurtz

Yes, it does work. Check your work or show it here if you can't find your error.